Results in Mathematics

, Volume 34, Issue 1–2, pp 169–173 | Cite as

Bernstein Inequality and Inverse Approximation Theorem in Modular Function Spaces

  • Julian Musielak
Research article


A Bernstein inequality and an inverse approximation theorem are proved in some classes of modular function spaces.

1991 MS Classification

41A17 41A27 46E30 

Keywords and Phrases

Approximation inverse approximation theorem Bernstein inequality Orlicz space modular space 


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  1. [1]
    N.I. Ahiezer, Lectures on Approximation Theory, Moscow, 1947 (in Russian).Google Scholar
  2. [2]
    P.L. Butzer, R.J. Nessel, Fourier Analysis and Approximation, Vol. I, Birkhäuser, Basel, and Academic Press, New York, 1971.CrossRefMATHGoogle Scholar
  3. [3]
    J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, Berlin, 1983.Google Scholar
  4. [4]
    J. Musielak, Approximation in modular function spaces, Funct. Approx. Comment. Math. 25 (1997), 45–57.MathSciNetMATHGoogle Scholar
  5. [5]
    A. Zygmund, Trigonometric Series, Vol. II, Cambridge Univ. Press, Cambridge, 1959.MATHGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Julian Musielak
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland

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